Nice OP, huh?
I don’t know how that happened.
Here’s the OP again:
I’m under the impression that:
Which one or more of my beliefs is wrong or oversimplified? What’s the resolution to these conflicting statements?
Electromagnetic radiation, which is induced by electric current, travels at the speed of light. Electricity is energy you get by moving electrons, not the electrons themselves, though. The actual electrons move somewhat slowly.
Electrical energy doesn’t travel in a wire at the speed of light. The number I remember, which is important in high speed devices where timing is critical, like computers, is about 8"/nanosecond which is about 2/3 the speed of light in a vacuum.
As was pointed out, the actual electrons move relatively slowly while an impulse of energy moves rapidly through them A crude analogy is a line of billiard balls with the first on struck by the cue ball. The first one hits the second, the second hits the third etc. The impulse moves rapidly down the line of balls but each ball only moves a little way.
Or another is a water wave. The wave travels at high speed while the water moves hardly at all.
And another one is water in a hose. Assuming the hose is full, if you turn on the faucet, water will come out the other end immediately, because the water from the faucet pushes on all the water in front of it. So you get water out the other end very quickly, but the water is not traveling very fast.
The speed is dependent on the dielectric insulating the conductors from each other.
For an overhead transmission line, the dielectric is air. The speed of light in air is 99.97% of the speed of light in a vacuum.
In a cable, things start to slow down appreciably. For polyethylene, e.g. in a high-voltage underground cable, the propagation speed is 0.65-0.70c. For PVC, which is used in household wiring, propagation speed is 0.60-0.64c.
In a chip using silicon dioxide as the dielectric, propagation is only at around 0.5c
Your talking about current, which doesn’t travel at the speed of light.
The message velocity (i.e. how fast the current will be felt once a potential has been set up) of a current is an appreciable fraction of the speed of light. The drift velocity (i.e. the average speed of an electron in the conducter) is absolutely tiny and more like an appreciable fraction of the speed of a slug.
I recall from high school physics that the electrons move at about 1 centimeter per second…or was it per hour? Either way, it was pretty slow.
An interesting tidbit, by the way: Even though the electrons move so slowly, it’s still possible (and in fact quite easy) to measure relativistic effects from their motion. The magnetic field around a wire is a purely relativistic effect. All moving objects obey relativity; it’s just that in slow-moving things, the effects are miniscule. But there are a lot of electrons in a wire, and it adds up.
electrons might move at any speed, might not even move at all ( if the wire is cut ) and the voltage will still travel at speed close to that of light, determined ( as mentioned above ) by dielectric constant of insulator.
i admit, that the role of electrons in electromagnetic waves is not clear to me. as EM waves can travel in perfect vacuum 
or they can travel in a wire
Well I look at it this way. EM waves move electrical charges and the place with by far the great majority of free electrical charges is in a conductor such as a wire. That’s why circuit analysis works.
I’m not sure who this post was directed at. But anyway. Drift velocity is indeed related to the speed of the electrons in the conductor. It’s important to be clear when talking about the term “average” here. The average is taken across the area of the conductor.
v = I / (Aρ)
where
v = drift velocity (ms[sup]-1[/sup])
I = current (A)
A = conductor area (m[sup]2[/sup])
ρ = free charge density (Cm[sup]-3[/sup])
Example:
Copper wire, I = 1 A, A = 1 mm[sup]2[/sup], ρ = 13.5x10[sup]9[/sup] Cm[sup]-3[/sup]
v = 7.4x10[sup]-5[/sup] ms[sup]-1[/sup]
That’s pretty slow. If you have a transmission line 1000 km long, it’d take only 3.3 ms for a signal to be transmitted from one end to the other, but 400 years for an individual electron to get from one end to the other.
Now, the point about averages. If the average is taken over time as well as area, the drift velocity in most situations ends up as zero. That’s because in any a.c. situation, the electrons just shuffle back and forth and never really move anywhere, even though they have a non-zero instantaneous drift velocity.
No. EM waves can’t travel at all in a perfect conductor, and can’t travel more than a few centimetres in something like copper or aluminium. Generally speaking, EM waves only travel in dielectrics, not conductors.
I think, Chronos, with all due respect, you’re either a bit confused here or else are trying to be deliberately confusing.
A moving charge creates a magnetic field. The strength of that field depends on the speed of the moving charge with respect to the observer.
So stationary observer A might measure a certain field strength, whilst moving observer B, moving at the same speed as the charge, measures a magnetic field strength of zero.
To characterise magnetism as “a purely relativistic effect” is misleading.
It’s a relative effect, in the same way that velocity is a relative effect.
Desmostylus, reread Chronos’ post then reread yours. All you’re doing is confirming what he said. Relative velocity is what Special Relativity is all about.
I couldn’t have expressed myself more poorly if I’d tried, which is unfortunate, because my complaint was only about Chronos’s choice of words and choice of example.
I’ll start again, beginning with the definition of the word relativistic:
So “relativistic” doesn’t necessarily mean relating to speeds approaching c, it can also mean relating to the theory of relativity.
Now, electromagnetism and special relativity are very closely related.
It would be strictly correct, but rather unhelpful, to describe anything having to do with electromagnetism as “relativistic”. All electrons are “relativistic”. A light bulb is “relativistic”. A piece of wire is “relativistic”. My car operates on “relativistic” principles, and so on.
And of course gravity and general relativity are also intertwined.
That means that my mouse pad shows “relativistic” behaviour, because it doesn’t float off into space.
I don’t believe that this use of the word “relativistic” is terribly useful, it only serves to confuse.
Secondly, on the choice of example. I don’t believe that the magnetic field generated by a moving charge is a particularly good demonstration of special relativity.
The relationship between current in a wire and the magnetic field around it is:
I = ∫B.dL.
Current, of course, can be regarded as the time rate of charge movement. But there’s nothing in that relationship that demonstrates the difference between Special Relativity and Galilean Relativity.
Indeed, the failure of Maxwell’s equations and Special Relativity to properly account for magnetic fields produced by moving charges will probably eventually prove to be the downfall of Special Relativity.
SR and Maxwell are “neat” mathematically, and are very good at describing how the physical universe operates, but fail to adequately describe both esoteric phenomena like the Aharonov-Bohm effect, and simple everyday things like two electrons moving past each other in space. In the latter example, why do the electrons suddenly behave as if there’s no such thing as a magnetic field? Whereas if one or both of them were contained to a wire, they would?
I did, in fact, mean “relativistic” as in “approaching the speed of light”, or “close enough to the speed of light that you can notice non-Galilean effects”. If you put Coulomb’s Law and the rules for relativity in a blender and mix for a few minutes, you’ll discover that two parallel wires with current going the same way will be attracted to each other, and by the experimentally-observed result, without ever explicitly putting in anything about magnetism. Magnetism follows necessarily from electrostatics, as a direct result of special relativity.
More detail on the relativistic derivation of magnetism: Suppose you have those two above-mentioned parallel wires with the same direction of movement. Now, put yourself in the frame of a nucleus in wire A. You see the nuclei in wire B at rest, but the electrons in wire B are moving relative to you. Since they’re moving, the distance between them is shorter, as measured by you on the nucleus, so the positively-charged nucleus sees the other wire as having a net negative charge, and is attracted to it. Meanwhile, an electron in wire A sees the B electrons at rest, but the B nuclei moving and Lorentz compressed, so it sees wire B as having a net positive charge, and is also attracted to it. Net result: Wire A is attracted to Wire B.
Don’t feel bad OP, a reporter for NPR news made the same mistake on 08/25/2003 when talking about the next generation power grid which would “control the flow of electrons, a commodity which travels at the speed of light”.
In electric circuits, the energy (the EM waves) don’t travel inside the wires. They travel in the space surrounding the wires. To oversimpify: the EM waves are connected to the wires in the same way that electrostatic fields are connected to the electrons. If you have a crowd of electrons then you have an e-field in the surrounding space, and if there are some density-waves moving through the population of electrons, then there are EM waves moving in the space surrounding those electrons.
One way that helps me think about this is to visualize coaxial cable rather than lamp cord.
If you drive a distant light bulb using coaxial cable, then you’ll find a strong e-field in the plastic insulation between the cable’s center conductor and its shield. You’ll also find a strong magnetic field in the same place… but no fields outside. The magnetic field looks like circles surrounding the center conductor, while the electric field is radial, with its field lines cutting across the magnetic field lines and touching down on the center and outer conductors. The electric and magnetic fields ARE THE ENERGY. The energy that lights the distant light bulb is travelling as EM fields in the plastic insulation. You can even multiply the field strengths together at every point in the cable, add them all up, and you end up with the wattage being delivered to the bulb. At the same time we also have electrons travelling in the center conductor, and more electrons travelling in the outer conductor. The population of electrons act as electric shields which keep the EM fields inside the cable.
So, if you use lamp cord to light a bulb, the electrons in the lamp cord act as electric shielding which forces the EM waves to follow the cable. The EM energy is like an invisible sausage with the pair of wires running down its center. In this case the “shielding” effect is inside-out. The sausage of EM energy can’t peel loose from the wire. If the wire turns, the EM-sausage is forced to follow.
Most people prefer to imagine that the electrons in the wire are carrying the energy directly. This erases all the weird concepts. But then certain things become hard to explain, such as the fact that the electrons wiggle back and forth within the metal while the energy flows rapidly forward. (That brings up another analogy: the electrons of the metal are like air molecules, while the travelling electrical energy is like sound waves …sort of… in an oversimplified way.)
The reporter should not be faulted. During the discussion of the blackout a friend of mine tabulated a half dozen quotations, from people who were either power company executives or electrical engineers who explained that electric power traveled at the speed of light and therefore they should not be faulted for not being able to contain the failure. That was exaggeration of course; the power travels at a good fraction of the speed of light, but so do the control signals. The plain fact is that the electric companies have no financial interest in spending billions to prevent disasters like that.
This is a nitpick but I’m gonna call you on this one.
If there are free electrons, and a potential difference(voltage), the electrons are moving in the wire…if the electrons have arranged themselves so that there is no longer a voltage difference in the wire, then they will not move at all. V=IR and all that…if I=0, then so does V.
I’m ignoring superconductors BTW…assume copper.